Z Procedure:

You are a quality control manager at a factory that produces lightbulbs. The company claims that the average lifespan of its lightbulbs is 1200 hours. You suspect that the actual average lifespan is less than 1200. To test this, you decide to take an SRS of 50 lightbulbs from the production line and measure their lifespans. The average lifespan of this sample is 1180 hours. From the historical data, you know the population standard deviation of the lifespan of these lightbulbs it's 100 hours.

(A) Let the mean be the true average lifespans of all lightbulbs in this company. Does the data provide evidence for your belief? Perform the 4-step testing procedures at a significance level set at 5%. You may find the p-value using Shiny App or R code.

(B) Find the 99% confidence interval for the mean. Interpret this confidence interval.

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